Related papers: Inversion of adjunction for higher rational singul…
We prove inversion of adjunction on log canonicity.
We prove the precise inversion of adjunction formula for quotient singularities. As an application, we prove the semi-continuity of minimal log discrepancies for hyperquotient singularities. This paper is a continuation of arXiv:2011.07300,…
We prove the precise inversion of adjunction formula for quotient singularities and klt Cartier divisors. As an application, we prove the semi-continuity of minimal log discrepancies for klt hyperquotient singularities.
We prove that the minimal exponent for local complete intersections satisfies an Inversion-of-Adjunction property. As a result, we also obtain the Inversion of Adjunction for higher Du Bois and higher rational singularities for local…
We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.
We prove the precise inversion of adjunction formula for finite linear group quotients of complete intersection varieties defined by semi-invariant equations. As an application, we prove the semi-continuity of minimal log discrepancies for…
We prove a precise inversion of adjunction formula for the log pair associated to a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded from above by…
We first announce our recent result on adjunction and inversion of adjunction. Then we clarify the relationship between our inversion of adjunction and Hacon's inversion of adjunction for log canonical centers of arbitrary codimension.
We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.
We prove several results about the behavior Du Bois singularities and Du Bois pairs in families. Some of these generalize existing statements about Du Bois singularities to the pair setting while others are new even in the non-pair setting.…
In this note we build on our previous work with Takehiko Yasuda to prove a precise version of inversion of adjunction for varieties which are local complete intersections.
This is a short note on the log canonical inversion of adjunction.
We prove Union-Closed sets conjecture.
By suitable examples we illustrate an algorithm for composition of inverse problems.
We prove that good quotients of algebraic varieties with 1-rational singularities also have 1-rational singularities. This refines a result of Boutot on rational singularities of good quotients.
We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.
In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational…
Upper moduli part of adjunction is introduced and its basic property are discussed. The moduli part satisfies the BP in the case of rational multiplicities and is nef in the maximal case.
We generalize the notions of F-regular and F-pure rings to pairs $(R,\a^t)$ of rings $R$ and ideals $\a \subset R$ with real exponent $t > 0$, and investigate these properties. These ``F-singularities of pairs'' correspond to singularities…
We analyze adjunction and inversion of adjunction for the $F$-purity of divisor pairs in characteristic $p > 0$. In this vein, we give a complete answer for principal divisors under $\mathbb{Q}$-Gorenstein assumptions but without…